Question

a certain standardized tests math scores have a bell - shaped distribution with a mean of 520 and a standard deviation of 119. complete parts (a) through (c). (a) what percentage of standardized test scores is between 401 and 639? (round to one decimal place as needed.)

Explanation:

Step1: Calculate z - scores

The formula for the z - score is $z=\frac{x-\mu}{\sigma}$, where $\mu$ is the mean, $\sigma$ is the standard deviation, and $x$ is the value from the data set.
For $x = 401$, $z_1=\frac{401 - 520}{119}=\frac{- 119}{119}=-1$.
For $x = 639$, $z_2=\frac{639 - 520}{119}=\frac{119}{119}=1$.

Step2: Use the standard normal distribution

The standard normal distribution table gives the cumulative probabilities for different z - scores. The cumulative probability for $z=-1$ is $P(Z < - 1)=0.1587$, and the cumulative probability for $z = 1$ is $P(Z < 1)=0.8413$.
The probability that $-1

Answer:

$68.3\%$